Meetings

Click on the theme item for the meeting plan for that theme.Click on the meeting item for references, exercises, and additional reading related to it.

**Theme 1 : Computability Theory**- 29 meetings- Meeting 01 : Mon, Jul 31, 08:00 am-08:50 am
- Meeting 02 : Tue, Aug 01, 12:00 pm-12:50 pm
- Meeting 03 : Thu, Aug 03, 11:00 am-11:50 am
- Meeting 04 : Fri, Aug 04, 10:00 am-10:50 am
- Meeting 05 : Mon, Aug 07, 08:00 am-08:50 am
- Meeting 06 : Tue, Aug 08, 12:00 pm-12:50 pm
- Meeting 07 : Thu, Aug 10, 11:00 am-11:50 am
- Meeting 08 : Fri, Aug 11, 10:00 am-10:50 am
- Meeting 09 : Mon, Aug 14, 08:00 am-08:50 am
- Meeting 10 : Thu, Aug 17, 11:00 am-11:50 am
- Meeting 11 : Fri, Aug 18, 10:00 am-10:50 am
- Meeting 12 : Sat, Aug 19, 03:00 pm-04:15 pm
- Meeting 13 : Mon, Aug 21, 08:00 am-08:50 am
- Meeting 14 : Tue, Aug 22, 12:00 pm-12:50 pm
- Meeting 15 : Thu, Aug 24, 11:00 am-11:50 am
- Meeting 16 : Fri, Aug 25, 10:00 am-10:50 am
- Meeting 17 : Mon, Aug 28, 08:00 am-08:50 am
- Meeting 18 : Tue, Aug 29, 12:00 pm-12:50 pm
- Meeting 19 : Thu, Aug 31, 11:00 am-11:50 am
- Meeting 20 : Fri, Sep 01, 10:00 am-10:50 am
- Meeting 21 : Mon, Sep 04, 08:00 am-08:50 am
- Meeting 22 : Tue, Sep 05, 12:00 pm-12:50 pm
- Meeting 23 : Thu, Sep 07, 11:00 am-11:50 am
- Meeting 24 : Sat, Sep 09, 10:00 am-10:50 am
- Meeting 25 : Mon, Sep 11, 08:00 am-08:50 am
- Meeting 26 : Tue, Sep 12, 12:00 pm-12:50 pm
- Meeting 27 : Thu, Sep 14, 11:00 am-11:50 am
- Meeting 28 : Fri, Sep 15, 10:00 am-10:50 am
- Meeting 29 : Mon, Sep 18, 08:00 am-08:50 am

Brief introduction to the course and the contents. Administrative Announcements. Grading policies. Languages vs Algorithmic Problems. Automata theory vs algorithms courses. Historical aspects of the idea of computation. Ruler and Compass problem. Hilbert's problem. Need of understanding computation in very formal terms. References Exercises Reading Brief introduction to the course and the contents. Administrative Announcements. Grading policies. Languages vs Algorithmic Problems. Automata theory vs algorithms courses. Historical aspects of the idea of computation. Ruler and Compass problem. Hilbert's problem. Need of understanding computation in very formal terms.References : None Problem of Searching the Treasure on the number line. Algorithms. Drawbacks. Diophantine problem. Formal model of computation. Post Systems, Mu-calculus, Lambda calculus. Turing machines. Formal Model of Turing machines. References Exercises Reading Problem of Searching the Treasure on the number line. Algorithms. Drawbacks. Diophantine problem. Formal model of computation. Post Systems, Mu-calculus, Lambda calculus. Turing machines. Formal Model of Turing machines.References : None Configurations of TM model. Acceptance of a string by Turing machines. Decidable, semi-decidable and undecidable. Robustness of the Turing machine model. Tape reduction theorem. Robustness of the Turing machine model. Multitape Turing machines, multi-head Turing machines. References Exercises Reading Configurations of TM model. Acceptance of a string by Turing machines. Decidable, semi-decidable and undecidable. Robustness of the Turing machine model. Tape reduction theorem. Robustness of the Turing machine model. Multitape Turing machines, multi-head Turing machines.References : None Encoding of Turing machines as strings. Universal Turing machine. References Exercises Reading Encoding of Turing machines as strings. Universal Turing machine.References : None Decidable Languages, Semi-Decidable Languages. Connections and structure. References Exercises Reading Decidable Languages, Semi-Decidable Languages. Connections and structure.References : None Story of infinity. Review of cantors diagonalization (1895). Undecidability of the halting problem (1936). References Exercises Reading Story of infinity. Review of cantors diagonalization (1895). Undecidability of the halting problem (1936).References : None Undecidability of Membership problem. Informal notion of reductions. Are there other undecidable problems. Examples of decidable problems. References Exercises Reading Undecidability of Membership problem. Informal notion of reductions. Are there other undecidable problems. Examples of decidable problems.References : None Examples of undecidable problems. One tool does it all. Undecidability of MP_101, EMPTY, TOTAL, FIN. References Exercises Reading Examples of undecidable problems. One tool does it all. Undecidability of MP_101, EMPTY, TOTAL, FIN.References : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None How do we prove that a language is not semi-decidable? HP-bar reduces to FIN. References Exercises Reading How do we prove that a language is not semi-decidable? HP-bar reduces to FIN.References : None Proof of Rice's First Theorem. Applications. Rice's Second Theorem. Proof and Applications. References Exercises Reading Proof of Rice's First Theorem. Applications. Rice's Second Theorem. Proof and Applications.References : None SD-completeness. CoSD-completeness. Hardness. MP is SD-complete. HP is SD-complete. References Exercises Reading SD-completeness. CoSD-completeness. Hardness. MP is SD-complete. HP is SD-complete.References : None Axioms and Rules of inteference. Proof system. Completeness, soundness. Peano's axioms. Godel's incompeteness Theorem. Turing's proof of the incompletness. References Exercises Reading Axioms and Rules of inteference. Proof system. Completeness, soundness. Peano's axioms. Godel's incompeteness Theorem. Turing's proof of the incompletness.References : None Proof of incompletenss theorem. References Exercises Reading Proof of incompletenss theorem.References : None Proof of incompletenss theorem. References Exercises Reading Proof of incompletenss theorem.References : None Quiz 1 References Exercises Reading Quiz 1References : None No lecture, yet to be compensated. References Exercises Reading No lecture, yet to be compensated.References : None Post's theorem. References Exercises Reading Post's theorem.References : None Post's theorem. References Exercises Reading Post's theorem.References : None MPXOR example. Oracle Turing machines. OTM for MPXOR. Definition of "semidecidable in A", "decidable in A". References Exercises Reading MPXOR example. Oracle Turing machines. OTM for MPXOR. Definition of "semidecidable in A", "decidable in A".References : None Turing reducibility. Connections to many-one reducibility. Sigma-i, Pi-i and Delta-i. Relation between these classes. Relativisation of proofs. References Exercises Reading Turing reducibility. Connections to many-one reducibility. Sigma-i, Pi-i and Delta-i. Relation between these classes. Relativisation of proofs.References : None Diagonalization is relativisable. MP^MP is complete for Sigma-2. Sigma-i cap Pi-i is exactly Delta-i. Separation of the levels of AH. References Exercises Reading Diagonalization is relativisable. MP^MP is complete for Sigma-2. Sigma-i cap Pi-i is exactly Delta-i. Separation of the levels of AH.References : None Characterization of the Arithmetic Hierarchy. Applications. MP, REG, DEC, TOTAL, FIN. References Exercises Reading Characterization of the Arithmetic Hierarchy. Applications. MP, REG, DEC, TOTAL, FIN.References : None Proof of the characterization. References Exercises Reading Proof of the characterization.References : None Proof of the characterization. FIN is Sigma-2 complete. References Exercises Reading Proof of the characterization. FIN is Sigma-2 complete.References : None FIN^HP is Sigma-2 complete. References Exercises Reading FIN^HP is Sigma-2 complete.References : None COF is Sigma-3 complete. References Exercises Reading COF is Sigma-3 complete.References : None No lecture. References Exercises Reading No lecture.References : None **Theme 2 : Time Complexity Classes**- 15 meetings- Meeting 30 : Tue, Sep 19, 12:00 pm-12:50 pm
- Meeting 31 : Thu, Sep 21, 11:00 am-11:50 am
- Meeting 32 : Mon, Sep 25, 08:00 am-08:50 am
- Meeting 33 : Tue, Sep 26, 12:00 pm-12:50 pm
- Meeting 34 : Tue, Sep 26, 06:00 pm-07:00 pm
- Meeting 35 : Fri, Sep 29, 10:00 am-10:50 am
- Meeting 36 : Mon, Oct 02, 08:00 am-08:50 am
- Meeting 37 : Tue, Oct 03, 12:00 pm-12:50 pm
- Meeting 38 : Thu, Oct 05, 11:00 am-11:50 am
- Meeting 39 : Fri, Oct 06, 10:00 am-10:50 am
- Meeting 40 : Sat, Oct 07, 11:00 am-11:50 am
- Meeting 41 : Mon, Oct 09, 08:00 am-08:50 am
- Meeting 42 : Tue, Oct 10, 12:00 pm-12:50 pm
- Meeting 43 : Thu, Oct 12, 11:00 am-11:50 am
- Meeting 44 : Fri, Oct 13, 10:00 am-10:50 am

Resource bounded computation. Blum's axiom. Examples and non-examples. Time, Space, Halt-Indicator. g-bounded complexity class. DTIME as a complexity class. References Exercises Reading Resource bounded computation. Blum's axiom. Examples and non-examples. Time, Space, Halt-Indicator. g-bounded complexity class. DTIME as a complexity class.References : None Borodin-Trankenbrot Gap theorem. Towards time hierarchy theorem. Weak, Weaker and Stronger versions. Discussions. References Exercises Reading Borodin-Trankenbrot Gap theorem. Towards time hierarchy theorem. Weak, Weaker and Stronger versions. Discussions.References : None Proof of the hierarchy theorem. Attempt 1. Failure. Fixing to attempt 2, tape reduction theorem. References Exercises Reading Proof of the hierarchy theorem. Attempt 1. Failure. Fixing to attempt 2, tape reduction theorem.References : None Optimality of tape reduction. The PALINDROME language. Hennie-Stearns theorem (statement) and discussion. References Exercises Reading Optimality of tape reduction. The PALINDROME language. Hennie-Stearns theorem (statement) and discussion.References : None Crossing sequence argument and limitation of 1-tape Turing machines. References Exercises Reading Crossing sequence argument and limitation of 1-tape Turing machines.References : None No lecture References Exercises Reading No lectureReferences : None No lecture References Exercises Reading No lectureReferences : None Notion of efficiency. Edmonds proposition. Discussion and the definition of class P, EXP. Basic simulations. Example problems - CLIQUE, REACH, INDSET, VC. References Exercises Reading Notion of efficiency. Edmonds proposition. Discussion and the definition of class P, EXP. Basic simulations. Example problems - CLIQUE, REACH, INDSET, VC.References : None More examples - COMPOSITE, CIRCUITS, CKTSAT, CVP, MINCKT, ANTHAKSHARI. Exponential time trivial algorithms. References Exercises Reading More examples - COMPOSITE, CIRCUITS, CKTSAT, CVP, MINCKT, ANTHAKSHARI. Exponential time trivial algorithms.References : None Graph Isomorphism. From the examples, the property of problems for "easily verifiable short certificates of membership". The class NP. Definition based on non-deterministic polytime Turing machines. References Exercises Reading Graph Isomorphism. From the examples, the property of problems for "easily verifiable short certificates of membership". The class NP. Definition based on non-deterministic polytime Turing machines.References : None Non-deterministic Algorithms. Correctness and Runtime arguments. Equivalence of the two definitions of NP. NP is contained in EXP. References Exercises Reading Non-deterministic Algorithms. Correctness and Runtime arguments. Equivalence of the two definitions of NP. NP is contained in EXP.References : None Padding arguments. NP=P implies NEXP=EXP. PRIMES and the class CoNP. CoNP is contained in EXP. P is contained in the intersection of NP and CoNP. Why complementation is a big deal. References Exercises Reading Padding arguments. NP=P implies NEXP=EXP. PRIMES and the class CoNP. CoNP is contained in EXP. P is contained in the intersection of NP and CoNP. Why complementation is a big deal.References : None TAUT, EXACT-CLIQUE. If NP=P, which languages have polynomial time algrithms. Oracle Turing machines. Non-deterministic oracle Turing machines. Polynomial hierarchy. References Exercises Reading TAUT, EXACT-CLIQUE. If NP=P, which languages have polynomial time algrithms. Oracle Turing machines. Non-deterministic oracle Turing machines. Polynomial hierarchy.References : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None **Theme 3 : Space Complexity Classes**- 9 meetings- Meeting 45 : Mon, Oct 16, 08:00 am-08:50 am
- Meeting 46 : Tue, Oct 17, 12:00 pm-12:50 pm
- Meeting 47 : Thu, Oct 19, 11:00 am-11:50 am
- Meeting 48 : Fri, Oct 20, 10:00 am-10:50 am
- Meeting 49 : Mon, Oct 23, 08:00 am-08:50 am
- Meeting 50 : Tue, Oct 24, 12:00 pm-12:50 pm
- Meeting 51 : Thu, Oct 26, 11:00 am-11:50 am
- Meeting 52 : Fri, Oct 27, 10:00 am-10:50 am
- Meeting 53 : Mon, Oct 30, 08:00 am-08:50 am

To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None To Be Announced References Exercises Reading To Be AnnouncedReferences : None **Theme 4 : Randomized Complexity Classes**- 10 meetings- Meeting 54 : Tue, Oct 31, 12:00 pm-12:50 pm
- Meeting 55 : Thu, Nov 02, 11:00 am-11:50 am
- Meeting 56 : Fri, Nov 03, 10:00 am-10:50 am
- Meeting 57 : Mon, Nov 06, 08:00 am-08:50 am
- Meeting 58 : Tue, Nov 07, 12:00 pm-12:50 pm
- Meeting 59 : Thu, Nov 09, 11:00 am-11:50 am
- Meeting 60 : Fri, Nov 10, 10:00 am-10:50 am
- Meeting 61 : Mon, Nov 13, 08:00 am-08:50 am
- Meeting 62 : Tue, Nov 14, 12:00 pm-12:50 pm
- Meeting 63 : Thu, Nov 16, 11:00 am-11:50 am

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